LMFDB - Embedded newform 8015.2.a.m.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.82956 q^{2} -1.24341 q^{3} +1.34731 q^{4} +1.00000 q^{5} +2.27489 q^{6} -1.00000 q^{7} +1.19414 q^{8} -1.45394 q^{9} +O(q^{10})$	\(q-1.82956 q^{2} -1.24341 q^{3} +1.34731 q^{4} +1.00000 q^{5} +2.27489 q^{6} -1.00000 q^{7} +1.19414 q^{8} -1.45394 q^{9} -1.82956 q^{10} -0.564870 q^{11} -1.67525 q^{12} -0.0201131 q^{13} +1.82956 q^{14} -1.24341 q^{15} -4.87938 q^{16} +1.60064 q^{17} +2.66007 q^{18} -4.90755 q^{19} +1.34731 q^{20} +1.24341 q^{21} +1.03347 q^{22} -5.79595 q^{23} -1.48481 q^{24} +1.00000 q^{25} +0.0367983 q^{26} +5.53806 q^{27} -1.34731 q^{28} +5.37206 q^{29} +2.27489 q^{30} -8.84014 q^{31} +6.53885 q^{32} +0.702364 q^{33} -2.92847 q^{34} -1.00000 q^{35} -1.95890 q^{36} +0.715882 q^{37} +8.97868 q^{38} +0.0250088 q^{39} +1.19414 q^{40} -5.89172 q^{41} -2.27489 q^{42} +6.24276 q^{43} -0.761054 q^{44} -1.45394 q^{45} +10.6041 q^{46} -9.83472 q^{47} +6.06705 q^{48} +1.00000 q^{49} -1.82956 q^{50} -1.99024 q^{51} -0.0270986 q^{52} -10.9228 q^{53} -10.1322 q^{54} -0.564870 q^{55} -1.19414 q^{56} +6.10208 q^{57} -9.82854 q^{58} -1.24664 q^{59} -1.67525 q^{60} +5.36485 q^{61} +16.1736 q^{62} +1.45394 q^{63} -2.20450 q^{64} -0.0201131 q^{65} -1.28502 q^{66} -12.2466 q^{67} +2.15655 q^{68} +7.20673 q^{69} +1.82956 q^{70} +2.72623 q^{71} -1.73621 q^{72} -2.51473 q^{73} -1.30975 q^{74} -1.24341 q^{75} -6.61198 q^{76} +0.564870 q^{77} -0.0457553 q^{78} -7.50967 q^{79} -4.87938 q^{80} -2.52425 q^{81} +10.7793 q^{82} -3.43447 q^{83} +1.67525 q^{84} +1.60064 q^{85} -11.4215 q^{86} -6.67967 q^{87} -0.674535 q^{88} +15.0223 q^{89} +2.66007 q^{90} +0.0201131 q^{91} -7.80893 q^{92} +10.9919 q^{93} +17.9933 q^{94} -4.90755 q^{95} -8.13046 q^{96} -6.47589 q^{97} -1.82956 q^{98} +0.821286 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) $ 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.82956	−1.29370	−0.646849	−	0.762618i	$-0.723914\pi$
$2$	−1.82956	−1.29370	−0.646849	+	0.762618i	$0.723914\pi$
$3$	−1.24341	−0.717882	−0.358941	−	0.933360i	$-0.616862\pi$
$3$	−1.24341	−0.717882	−0.358941	+	0.933360i	$0.616862\pi$
$4$	1.34731	0.673654
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.27489	0.928722
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.19414	0.422193
$9$	−1.45394	−0.484646
$10$	−1.82956	−0.578559
$11$	−0.564870	−0.170315	−0.0851574	−	0.996368i	$-0.527139\pi$
$11$	−0.564870	−0.170315	−0.0851574	+	0.996368i	$0.527139\pi$
$12$	−1.67525	−0.483604
$13$	−0.0201131	−0.00557838	−0.00278919	−	0.999996i	$-0.500888\pi$
$13$	−0.0201131	−0.00557838	−0.00278919	+	0.999996i	$0.500888\pi$
$14$	1.82956	0.488972
$15$	−1.24341	−0.321046
$16$	−4.87938	−1.21984
$17$	1.60064	0.388211	0.194106	−	0.980981i	$-0.437820\pi$
$17$	1.60064	0.388211	0.194106	+	0.980981i	$0.437820\pi$
$18$	2.66007	0.626985
$19$	−4.90755	−1.12587	−0.562934	−	0.826502i	$-0.690328\pi$
$19$	−4.90755	−1.12587	−0.562934	+	0.826502i	$0.690328\pi$
$20$	1.34731	0.301267
$21$	1.24341	0.271334
$22$	1.03347	0.220336
$23$	−5.79595	−1.20854	−0.604269	−	0.796780i	$-0.706535\pi$
$23$	−5.79595	−1.20854	−0.604269	+	0.796780i	$0.706535\pi$
$24$	−1.48481	−0.303085
$25$	1.00000	0.200000
$26$	0.0367983	0.00721674
$27$	5.53806	1.06580
$28$	−1.34731	−0.254617
$29$	5.37206	0.997567	0.498784	−	0.866727i	$-0.333780\pi$
$29$	5.37206	0.997567	0.498784	+	0.866727i	$0.333780\pi$
$30$	2.27489	0.415337
$31$	−8.84014	−1.58774	−0.793868	−	0.608090i	$-0.791936\pi$
$31$	−8.84014	−1.58774	−0.793868	+	0.608090i	$0.791936\pi$
$32$	6.53885	1.15592
$33$	0.702364	0.122266
$34$	−2.92847	−0.502228
$35$	−1.00000	−0.169031
$36$	−1.95890	−0.326484
$37$	0.715882	0.117690	0.0588451	−	0.998267i	$-0.481258\pi$
$37$	0.715882	0.117690	0.0588451	+	0.998267i	$0.481258\pi$
$38$	8.97868	1.45653
$39$	0.0250088	0.00400462
$40$	1.19414	0.188810
$41$	−5.89172	−0.920132	−0.460066	−	0.887885i	$-0.652174\pi$
$41$	−5.89172	−0.920132	−0.460066	+	0.887885i	$0.652174\pi$
$42$	−2.27489	−0.351024
$43$	6.24276	0.952012	0.476006	−	0.879442i	$-0.342084\pi$
$43$	6.24276	0.952012	0.476006	+	0.879442i	$0.342084\pi$
$44$	−0.761054	−0.114733
$45$	−1.45394	−0.216740
$46$	10.6041	1.56348
$47$	−9.83472	−1.43454	−0.717270	−	0.696795i	$-0.754609\pi$
$47$	−9.83472	−1.43454	−0.717270	+	0.696795i	$0.754609\pi$
$48$	6.06705	0.875704
$49$	1.00000	0.142857
$50$	−1.82956	−0.258740
$51$	−1.99024	−0.278690
$52$	−0.0270986	−0.00375790
$53$	−10.9228	−1.50036	−0.750178	−	0.661235i	$-0.770032\pi$
$53$	−10.9228	−1.50036	−0.750178	+	0.661235i	$0.770032\pi$
$54$	−10.1322	−1.37882
$55$	−0.564870	−0.0761671
$56$	−1.19414	−0.159574
$57$	6.10208	0.808241
$58$	−9.82854	−1.29055
$59$	−1.24664	−0.162298	−0.0811492	−	0.996702i	$-0.525859\pi$
$59$	−1.24664	−0.162298	−0.0811492	+	0.996702i	$0.525859\pi$
$60$	−1.67525	−0.216274
$61$	5.36485	0.686899	0.343450	−	0.939171i	$-0.388405\pi$
$61$	5.36485	0.686899	0.343450	+	0.939171i	$0.388405\pi$
$62$	16.1736	2.05405
$63$	1.45394	0.183179
$64$	−2.20450	−0.275563
$65$	−0.0201131	−0.00249473
$66$	−1.28502	−0.158175
$67$	−12.2466	−1.49616	−0.748078	−	0.663611i	$-0.769023\pi$
$67$	−12.2466	−1.49616	−0.748078	+	0.663611i	$0.769023\pi$
$68$	2.15655	0.261520
$69$	7.20673	0.867588
$70$	1.82956	0.218675
$71$	2.72623	0.323544	0.161772	−	0.986828i	$-0.448279\pi$
$71$	2.72623	0.323544	0.161772	+	0.986828i	$0.448279\pi$
$72$	−1.73621	−0.204614
$73$	−2.51473	−0.294327	−0.147163	−	0.989112i	$-0.547014\pi$
$73$	−2.51473	−0.294327	−0.147163	+	0.989112i	$0.547014\pi$
$74$	−1.30975	−0.152256
$75$	−1.24341	−0.143576
$76$	−6.61198	−0.758446
$77$	0.564870	0.0643729
$78$	−0.0457553	−0.00518077
$79$	−7.50967	−0.844904	−0.422452	−	0.906385i	$-0.638830\pi$
$79$	−7.50967	−0.844904	−0.422452	+	0.906385i	$0.638830\pi$
$80$	−4.87938	−0.545531
$81$	−2.52425	−0.280472
$82$	10.7793	1.19037
$83$	−3.43447	−0.376982	−0.188491	−	0.982075i	$-0.560360\pi$
$83$	−3.43447	−0.376982	−0.188491	+	0.982075i	$0.560360\pi$
$84$	1.67525	0.182785
$85$	1.60064	0.173613
$86$	−11.4215	−1.23162
$87$	−6.67967	−0.716135
$88$	−0.674535	−0.0719057
$89$	15.0223	1.59236	0.796181	−	0.605059i	$-0.206850\pi$
$89$	15.0223	1.59236	0.796181	+	0.605059i	$0.206850\pi$
$90$	2.66007	0.280396
$91$	0.0201131	0.00210843
$92$	−7.80893	−0.814137
$93$	10.9919	1.13981
$94$	17.9933	1.85586
$95$	−4.90755	−0.503504
$96$	−8.13046	−0.829811
$97$	−6.47589	−0.657527	−0.328763	−	0.944412i	$-0.606632\pi$
$97$	−6.47589	−0.657527	−0.328763	+	0.944412i	$0.606632\pi$
$98$	−1.82956	−0.184814
$99$	0.821286	0.0825424
$100$	1.34731	0.134731
$101$	14.3789	1.43076	0.715379	−	0.698736i	$-0.246254\pi$
$101$	14.3789	1.43076	0.715379	+	0.698736i	$0.246254\pi$
$102$	3.64128	0.360541
$103$	6.39271	0.629893	0.314946	−	0.949109i	$-0.398013\pi$
$103$	6.39271	0.629893	0.314946	+	0.949109i	$0.398013\pi$
$104$	−0.0240180	−0.00235516
$105$	1.24341	0.121344
$106$	19.9839	1.94101
$107$	6.07116	0.586921	0.293460	−	0.955971i	$-0.405193\pi$
$107$	6.07116	0.586921	0.293460	+	0.955971i	$0.405193\pi$
$108$	7.46147	0.717980
$109$	1.99421	0.191011	0.0955054	−	0.995429i	$-0.469553\pi$
$109$	1.99421	0.191011	0.0955054	+	0.995429i	$0.469553\pi$
$110$	1.03347	0.0985372
$111$	−0.890133	−0.0844877
$112$	4.87938	0.461058
$113$	13.1823	1.24009	0.620043	−	0.784567i	$-0.287115\pi$
$113$	13.1823	1.24009	0.620043	+	0.784567i	$0.287115\pi$
$114$	−11.1642	−1.04562
$115$	−5.79595	−0.540475
$116$	7.23783	0.672015
$117$	0.0292433	0.00270354
$118$	2.28080	0.209965
$119$	−1.60064	−0.146730
$120$	−1.48481	−0.135544
$121$	−10.6809	−0.970993
$122$	−9.81535	−0.888640
$123$	7.32581	0.660546
$124$	−11.9104	−1.06959
$125$	1.00000	0.0894427
$126$	−2.66007	−0.236978
$127$	−8.05565	−0.714824	−0.357412	−	0.933947i	$-0.616341\pi$
$127$	−8.05565	−0.714824	−0.357412	+	0.933947i	$0.616341\pi$
$128$	−9.04443	−0.799422
$129$	−7.76230	−0.683432
$130$	0.0367983	0.00322743
$131$	5.89337	0.514906	0.257453	−	0.966291i	$-0.417117\pi$
$131$	5.89337	0.514906	0.257453	+	0.966291i	$0.417117\pi$
$132$	0.946300	0.0823649
$133$	4.90755	0.425538
$134$	22.4059	1.93557
$135$	5.53806	0.476640
$136$	1.91139	0.163900
$137$	6.10766	0.521812	0.260906	−	0.965364i	$-0.415979\pi$
$137$	6.10766	0.521812	0.260906	+	0.965364i	$0.415979\pi$
$138$	−13.1852	−1.12240
$139$	−12.3165	−1.04467	−0.522336	−	0.852740i	$-0.674939\pi$
$139$	−12.3165	−1.04467	−0.522336	+	0.852740i	$0.674939\pi$
$140$	−1.34731	−0.113868
$141$	12.2286	1.02983
$142$	−4.98781	−0.418568
$143$	0.0113613	0.000950081 0
$144$	7.09431	0.591193
$145$	5.37206	0.446126
$146$	4.60086	0.380770
$147$	−1.24341	−0.102555
$148$	0.964514	0.0792825
$149$	5.57753	0.456929	0.228464	−	0.973552i	$-0.426630\pi$
$149$	5.57753	0.456929	0.228464	+	0.973552i	$0.426630\pi$
$150$	2.27489	0.185744
$151$	−5.55572	−0.452118	−0.226059	−	0.974114i	$-0.572584\pi$
$151$	−5.55572	−0.452118	−0.226059	+	0.974114i	$0.572584\pi$
$152$	−5.86031	−0.475334
$153$	−2.32723	−0.188145
$154$	−1.03347	−0.0832791
$155$	−8.84014	−0.710057
$156$	0.0336946	0.00269773
$157$	−2.74454	−0.219038	−0.109519	−	0.993985i	$-0.534931\pi$
$157$	−2.74454	−0.219038	−0.109519	+	0.993985i	$0.534931\pi$
$158$	13.7394	1.09305
$159$	13.5814	1.07708
$160$	6.53885	0.516942
$161$	5.79595	0.456785
$162$	4.61828	0.362846
$163$	−20.4315	−1.60032	−0.800159	−	0.599788i	$-0.795252\pi$
$163$	−20.4315	−1.60032	−0.800159	+	0.599788i	$0.795252\pi$
$164$	−7.93796	−0.619850
$165$	0.702364	0.0546789
$166$	6.28359	0.487701
$167$	15.9874	1.23714	0.618571	−	0.785729i	$-0.287712\pi$
$167$	15.9874	1.23714	0.618571	+	0.785729i	$0.287712\pi$
$168$	1.48481	0.114555
$169$	−12.9996	−0.999969
$170$	−2.92847	−0.224603
$171$	7.13527	0.545648
$172$	8.41092	0.641327
$173$	−13.1973	−1.00338	−0.501688	−	0.865049i	$-0.667287\pi$
$173$	−13.1973	−1.00338	−0.501688	+	0.865049i	$0.667287\pi$
$174$	12.2209	0.926463
$175$	−1.00000	−0.0755929
$176$	2.75621	0.207757
$177$	1.55008	0.116511
$178$	−27.4843	−2.06003
$179$	−19.7243	−1.47427	−0.737133	−	0.675747i	$-0.763821\pi$
$179$	−19.7243	−1.47427	−0.737133	+	0.675747i	$0.763821\pi$
$180$	−1.95890	−0.146008
$181$	25.2155	1.87426	0.937128	−	0.348987i	$-0.113474\pi$
$181$	25.2155	1.87426	0.937128	+	0.348987i	$0.113474\pi$
$182$	−0.0367983	−0.00272767
$183$	−6.67070	−0.493112
$184$	−6.92119	−0.510237
$185$	0.715882	0.0526327
$186$	−20.1104	−1.47457
$187$	−0.904152	−0.0661181
$188$	−13.2504	−0.966384
$189$	−5.53806	−0.402835
$190$	8.97868	0.651382
$191$	−10.5071	−0.760265	−0.380132	−	0.924932i	$-0.624122\pi$
$191$	−10.5071	−0.760265	−0.380132	+	0.924932i	$0.624122\pi$
$192$	2.74109	0.197821
$193$	−6.19166	−0.445685	−0.222843	−	0.974854i	$-0.571534\pi$
$193$	−6.19166	−0.445685	−0.222843	+	0.974854i	$0.571534\pi$
$194$	11.8481	0.850641
$195$	0.0250088	0.00179092
$196$	1.34731	0.0962363
$197$	−10.9173	−0.777823	−0.388911	−	0.921275i	$-0.627149\pi$
$197$	−10.9173	−0.777823	−0.388911	+	0.921275i	$0.627149\pi$
$198$	−1.50260	−0.106785
$199$	12.9222	0.916034	0.458017	−	0.888944i	$-0.348560\pi$
$199$	12.9222	0.916034	0.458017	+	0.888944i	$0.348560\pi$
$200$	1.19414	0.0844386
$201$	15.2275	1.07406
$202$	−26.3072	−1.85097
$203$	−5.37206	−0.377045
$204$	−2.68147	−0.187741
$205$	−5.89172	−0.411495
$206$	−11.6959	−0.814891
$207$	8.42695	0.585713
$208$	0.0981396	0.00680476
$209$	2.77213	0.191752
$210$	−2.27489	−0.156983
$211$	25.6595	1.76647	0.883236	−	0.468929i	$-0.155360\pi$
$211$	25.6595	1.76647	0.883236	+	0.468929i	$0.155360\pi$
$212$	−14.7163	−1.01072
$213$	−3.38981	−0.232266
$214$	−11.1076	−0.759298
$215$	6.24276	0.425753
$216$	6.61323	0.449973
$217$	8.84014	0.600108
$218$	−3.64854	−0.247110
$219$	3.12683	0.211292
$220$	−0.761054	−0.0513103
$221$	−0.0321939	−0.00216559
$222$	1.62856	0.109302
$223$	−24.1017	−1.61397	−0.806984	−	0.590573i	$-0.798902\pi$
$223$	−24.1017	−1.61397	−0.806984	+	0.590573i	$0.798902\pi$
$224$	−6.53885	−0.436895
$225$	−1.45394	−0.0969292
$226$	−24.1179	−1.60430
$227$	10.9844	0.729062	0.364531	−	0.931191i	$-0.381229\pi$
$227$	10.9844	0.729062	0.364531	+	0.931191i	$0.381229\pi$
$228$	8.22138	0.544474
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	10.6041	0.699211
$231$	−0.702364	−0.0462121
$232$	6.41501	0.421166
$233$	15.5692	1.01997	0.509986	−	0.860183i	$-0.329651\pi$
$233$	15.5692	1.01997	0.509986	+	0.860183i	$0.329651\pi$
$234$	−0.0535025	−0.00349757
$235$	−9.83472	−0.641546
$236$	−1.67960	−0.109333
$237$	9.33758	0.606541
$238$	2.92847	0.189824
$239$	8.28008	0.535594	0.267797	−	0.963475i	$-0.413704\pi$
$239$	8.28008	0.535594	0.267797	+	0.963475i	$0.413704\pi$
$240$	6.06705	0.391627
$241$	−2.10129	−0.135356	−0.0676780	−	0.997707i	$-0.521559\pi$
$241$	−2.10129	−0.135356	−0.0676780	+	0.997707i	$0.521559\pi$
$242$	19.5414	1.25617
$243$	−13.4755	−0.864454
$244$	7.22811	0.462732
$245$	1.00000	0.0638877
$246$	−13.4030	−0.854546
$247$	0.0987063	0.00628053
$248$	−10.5564	−0.670331
$249$	4.27045	0.270629
$250$	−1.82956	−0.115712
$251$	8.46334	0.534202	0.267101	−	0.963669i	$-0.413934\pi$
$251$	8.46334	0.534202	0.267101	+	0.963669i	$0.413934\pi$
$252$	1.95890	0.123399
$253$	3.27396	0.205832
$254$	14.7383	0.924766
$255$	−1.99024	−0.124634
$256$	20.9564	1.30977
$257$	−20.5818	−1.28386	−0.641928	−	0.766765i	$-0.721865\pi$
$257$	−20.5818	−1.28386	−0.641928	+	0.766765i	$0.721865\pi$
$258$	14.2016	0.884155
$259$	−0.715882	−0.0444827
$260$	−0.0270986	−0.00168058
$261$	−7.81065	−0.483467
$262$	−10.7823	−0.666133
$263$	−8.40709	−0.518403	−0.259202	−	0.965823i	$-0.583459\pi$
$263$	−8.40709	−0.518403	−0.259202	+	0.965823i	$0.583459\pi$
$264$	0.838722	0.0516198
$265$	−10.9228	−0.670980
$266$	−8.97868	−0.550518
$267$	−18.6788	−1.14313
$268$	−16.4999	−1.00789
$269$	−9.49842	−0.579129	−0.289565	−	0.957158i	$-0.593511\pi$
$269$	−9.49842	−0.579129	−0.289565	+	0.957158i	$0.593511\pi$
$270$	−10.1322	−0.616628
$271$	17.5100	1.06366	0.531828	−	0.846853i	$-0.321505\pi$
$271$	17.5100	1.06366	0.531828	+	0.846853i	$0.321505\pi$
$272$	−7.81011	−0.473558
$273$	−0.0250088	−0.00151360
$274$	−11.1744	−0.675067
$275$	−0.564870	−0.0340630
$276$	9.70968	0.584454
$277$	−13.0456	−0.783833	−0.391917	−	0.920001i	$-0.628188\pi$
$277$	−13.0456	−0.783833	−0.391917	+	0.920001i	$0.628188\pi$
$278$	22.5338	1.35149
$279$	12.8530	0.769490
$280$	−1.19414	−0.0713637
$281$	19.2736	1.14976	0.574882	−	0.818236i	$-0.305048\pi$
$281$	19.2736	1.14976	0.574882	+	0.818236i	$0.305048\pi$
$282$	−22.3729	−1.33229
$283$	20.5653	1.22248	0.611240	−	0.791445i	$-0.290671\pi$
$283$	20.5653	1.22248	0.611240	+	0.791445i	$0.290671\pi$
$284$	3.67307	0.217956
$285$	6.10208	0.361456
$286$	−0.0207863	−0.00122912
$287$	5.89172	0.347777
$288$	−9.50709	−0.560210
$289$	−14.4380	−0.849292
$290$	−9.82854	−0.577152
$291$	8.05217	0.472026
$292$	−3.38811	−0.198274
$293$	−24.3683	−1.42361	−0.711805	−	0.702377i	$-0.752122\pi$
$293$	−24.3683	−1.42361	−0.711805	+	0.702377i	$0.752122\pi$
$294$	2.27489	0.132675
$295$	−1.24664	−0.0725820
$296$	0.854865	0.0496880
$297$	−3.12828	−0.181521
$298$	−10.2045	−0.591128
$299$	0.116575	0.00674169
$300$	−1.67525	−0.0967208
$301$	−6.24276	−0.359827
$302$	10.1646	0.584904
$303$	−17.8789	−1.02712
$304$	23.9458	1.37338
$305$	5.36485	0.307191
$306$	4.25781	0.243403
$307$	−7.67428	−0.437995	−0.218997	−	0.975725i	$-0.570279\pi$
$307$	−7.67428	−0.437995	−0.218997	+	0.975725i	$0.570279\pi$
$308$	0.761054	0.0433651
$309$	−7.94875	−0.452189
$310$	16.1736	0.918600
$311$	−28.4346	−1.61238	−0.806189	−	0.591658i	$-0.798474\pi$
$311$	−28.4346	−1.61238	−0.806189	+	0.591658i	$0.798474\pi$
$312$	0.0298641	0.00169072
$313$	−9.24608	−0.522620	−0.261310	−	0.965255i	$-0.584154\pi$
$313$	−9.24608	−0.522620	−0.261310	+	0.965255i	$0.584154\pi$
$314$	5.02132	0.283369
$315$	1.45394	0.0819201
$316$	−10.1178	−0.569173
$317$	6.20120	0.348294	0.174147	−	0.984720i	$-0.444283\pi$
$317$	6.20120	0.348294	0.174147	+	0.984720i	$0.444283\pi$
$318$	−24.8481	−1.39341
$319$	−3.03452	−0.169900
$320$	−2.20450	−0.123235
$321$	−7.54892	−0.421340
$322$	−10.6041	−0.590941
$323$	−7.85520	−0.437075
$324$	−3.40094	−0.188941
$325$	−0.0201131	−0.00111568
$326$	37.3807	2.07033
$327$	−2.47962	−0.137123
$328$	−7.03555	−0.388473
$329$	9.83472	0.542205
$330$	−1.28502	−0.0707380
$331$	26.9506	1.48134	0.740671	−	0.671868i	$-0.234508\pi$
$331$	26.9506	1.48134	0.740671	+	0.671868i	$0.234508\pi$
$332$	−4.62729	−0.253956
$333$	−1.04085	−0.0570381
$334$	−29.2500	−1.60049
$335$	−12.2466	−0.669101
$336$	−6.06705	−0.330985
$337$	−20.3198	−1.10689	−0.553446	−	0.832885i	$-0.686687\pi$
$337$	−20.3198	−1.10689	−0.553446	+	0.832885i	$0.686687\pi$
$338$	23.7836	1.29366
$339$	−16.3910	−0.890236
$340$	2.15655	0.116955
$341$	4.99353	0.270415
$342$	−13.0544	−0.705903
$343$	−1.00000	−0.0539949
$344$	7.45475	0.401933
$345$	7.20673	0.387997
$346$	24.1454	1.29807
$347$	19.8228	1.06415	0.532073	−	0.846699i	$-0.321413\pi$
$347$	19.8228	1.06415	0.532073	+	0.846699i	$0.321413\pi$
$348$	−8.99957	−0.482427
$349$	25.1392	1.34567	0.672834	−	0.739793i	$-0.265077\pi$
$349$	25.1392	1.34567	0.672834	+	0.739793i	$0.265077\pi$
$350$	1.82956	0.0977944
$351$	−0.111388	−0.00594544
$352$	−3.69360	−0.196870
$353$	−33.5103	−1.78357	−0.891787	−	0.452455i	$-0.850548\pi$
$353$	−33.5103	−1.78357	−0.891787	+	0.452455i	$0.850548\pi$
$354$	−2.83597	−0.150730
$355$	2.72623	0.144693
$356$	20.2397	1.07270
$357$	1.99024	0.105335
$358$	36.0870	1.90726
$359$	−9.12022	−0.481347	−0.240673	−	0.970606i	$-0.577368\pi$
$359$	−9.12022	−0.481347	−0.240673	+	0.970606i	$0.577368\pi$
$360$	−1.73621	−0.0915062
$361$	5.08403	0.267580
$362$	−46.1334	−2.42472
$363$	13.2807	0.697058
$364$	0.0270986	0.00142035
$365$	−2.51473	−0.131627
$366$	12.2045	0.637938
$367$	−5.29822	−0.276565	−0.138283	−	0.990393i	$-0.544158\pi$
$367$	−5.29822	−0.276565	−0.138283	+	0.990393i	$0.544158\pi$
$368$	28.2806	1.47423
$369$	8.56619	0.445938
$370$	−1.30975	−0.0680908
$371$	10.9228	0.567082
$372$	14.8095	0.767835
$373$	12.2394	0.633730	0.316865	−	0.948471i	$-0.397370\pi$
$373$	12.2394	0.633730	0.316865	+	0.948471i	$0.397370\pi$
$374$	1.65420	0.0855369
$375$	−1.24341	−0.0642093
$376$	−11.7441	−0.605653
$377$	−0.108049	−0.00556481
$378$	10.1322	0.521146
$379$	14.7547	0.757900	0.378950	−	0.925417i	$-0.376285\pi$
$379$	14.7547	0.757900	0.378950	+	0.925417i	$0.376285\pi$
$380$	−6.61198	−0.339187
$381$	10.0165	0.513159
$382$	19.2234	0.983553
$383$	−1.78796	−0.0913607	−0.0456804	−	0.998956i	$-0.514546\pi$
$383$	−1.78796	−0.0913607	−0.0456804	+	0.998956i	$0.514546\pi$
$384$	11.2459	0.573890
$385$	0.564870	0.0287884
$386$	11.3280	0.576582
$387$	−9.07659	−0.461389
$388$	−8.72502	−0.442946
$389$	6.87390	0.348521	0.174260	−	0.984700i	$-0.444247\pi$
$389$	6.87390	0.348521	0.174260	+	0.984700i	$0.444247\pi$
$390$	−0.0457553	−0.00231691
$391$	−9.27721	−0.469169
$392$	1.19414	0.0603133
$393$	−7.32786	−0.369641
$394$	19.9738	1.00627
$395$	−7.50967	−0.377852
$396$	1.10653	0.0556050
$397$	18.9669	0.951919	0.475959	−	0.879467i	$-0.342101\pi$
$397$	18.9669	0.951919	0.475959	+	0.879467i	$0.342101\pi$
$398$	−23.6421	−1.18507
$399$	−6.10208	−0.305486
$400$	−4.87938	−0.243969
$401$	20.3948	1.01847	0.509234	−	0.860628i	$-0.329929\pi$
$401$	20.3948	1.01847	0.509234	+	0.860628i	$0.329929\pi$
$402$	−27.8596	−1.38951
$403$	0.177803	0.00885700
$404$	19.3729	0.963836
$405$	−2.52425	−0.125431
$406$	9.82854	0.487782
$407$	−0.404380	−0.0200444
$408$	−2.37663	−0.117661
$409$	36.2095	1.79045	0.895223	−	0.445619i	$-0.147017\pi$
$409$	36.2095	1.79045	0.895223	+	0.445619i	$0.147017\pi$
$410$	10.7793	0.532351
$411$	−7.59430	−0.374599
$412$	8.61296	0.424330
$413$	1.24664	0.0613430
$414$	−15.4176	−0.757736
$415$	−3.43447	−0.168592
$416$	−0.131517	−0.00644815
$417$	15.3144	0.749951
$418$	−5.07179	−0.248069
$419$	−21.3759	−1.04428	−0.522140	−	0.852860i	$-0.674866\pi$
$419$	−21.3759	−1.04428	−0.522140	+	0.852860i	$0.674866\pi$
$420$	1.67525	0.0817440
$421$	15.5247	0.756626	0.378313	−	0.925678i	$-0.376504\pi$
$421$	15.5247	0.756626	0.378313	+	0.925678i	$0.376504\pi$
$422$	−46.9457	−2.28528
$423$	14.2991	0.695244
$424$	−13.0433	−0.633440
$425$	1.60064	0.0776423
$426$	6.20188	0.300482
$427$	−5.36485	−0.259623
$428$	8.17972	0.395382
$429$	−0.0141267	−0.000682046 0
$430$	−11.4215	−0.550796
$431$	23.4967	1.13180	0.565899	−	0.824474i	$-0.308529\pi$
$431$	23.4967	1.13180	0.565899	+	0.824474i	$0.308529\pi$
$432$	−27.0223	−1.30011
$433$	−30.8636	−1.48321	−0.741605	−	0.670837i	$-0.765935\pi$
$433$	−30.8636	−1.48321	−0.741605	+	0.670837i	$0.765935\pi$
$434$	−16.1736	−0.776358
$435$	−6.67967	−0.320265
$436$	2.68682	0.128675
$437$	28.4439	1.36066
$438$	−5.72074	−0.273348
$439$	−19.7663	−0.943392	−0.471696	−	0.881761i	$-0.656358\pi$
$439$	−19.7663	−0.943392	−0.471696	+	0.881761i	$0.656358\pi$
$440$	−0.674535	−0.0321572
$441$	−1.45394	−0.0692351
$442$	0.0589007	0.00280162
$443$	−13.2831	−0.631098	−0.315549	−	0.948909i	$-0.602189\pi$
$443$	−13.2831	−0.631098	−0.315549	+	0.948909i	$0.602189\pi$
$444$	−1.19928	−0.0569155
$445$	15.0223	0.712126
$446$	44.0956	2.08799
$447$	−6.93514	−0.328021
$448$	2.20450	0.104153
$449$	−30.2612	−1.42811	−0.714057	−	0.700087i	$-0.753144\pi$
$449$	−30.2612	−1.42811	−0.714057	+	0.700087i	$0.753144\pi$
$450$	2.66007	0.125397
$451$	3.32806	0.156712
$452$	17.7606	0.835390
$453$	6.90803	0.324567
$454$	−20.0967	−0.943186
$455$	0.0201131	0.000942919 0
$456$	7.28675	0.341234
$457$	0.664749	0.0310956	0.0155478	−	0.999879i	$-0.495051\pi$
$457$	0.664749	0.0310956	0.0155478	+	0.999879i	$0.495051\pi$
$458$	1.82956	0.0854900
$459$	8.86442	0.413756
$460$	−7.80893	−0.364093
$461$	−18.8380	−0.877375	−0.438687	−	0.898640i	$-0.644556\pi$
$461$	−18.8380	−0.877375	−0.438687	+	0.898640i	$0.644556\pi$
$462$	1.28502	0.0597845
$463$	−9.87148	−0.458767	−0.229383	−	0.973336i	$-0.573671\pi$
$463$	−9.87148	−0.458767	−0.229383	+	0.973336i	$0.573671\pi$
$464$	−26.2123	−1.21688
$465$	10.9919	0.509737
$466$	−28.4848	−1.31953
$467$	9.73049	0.450274	0.225137	−	0.974327i	$-0.427717\pi$
$467$	9.73049	0.450274	0.225137	+	0.974327i	$0.427717\pi$
$468$	0.0393997	0.00182125
$469$	12.2466	0.565494
$470$	17.9933	0.829967
$471$	3.41258	0.157243
$472$	−1.48866	−0.0685212
$473$	−3.52635	−0.162142
$474$	−17.0837	−0.784681
$475$	−4.90755	−0.225174
$476$	−2.15655	−0.0988454
$477$	15.8810	0.727142
$478$	−15.1489	−0.692897
$479$	−26.8037	−1.22469	−0.612346	−	0.790590i	$-0.709774\pi$
$479$	−26.8037	−1.22469	−0.612346	+	0.790590i	$0.709774\pi$
$480$	−8.13046	−0.371103
$481$	−0.0143986	−0.000656522 0
$482$	3.84445	0.175110
$483$	−7.20673	−0.327917
$484$	−14.3905	−0.654113
$485$	−6.47589	−0.294055
$486$	24.6543	1.11834
$487$	37.2135	1.68631	0.843153	−	0.537674i	$-0.180697\pi$
$487$	37.2135	1.68631	0.843153	+	0.537674i	$0.180697\pi$
$488$	6.40640	0.290004
$489$	25.4047	1.14884
$490$	−1.82956	−0.0826513
$491$	−3.74904	−0.169192	−0.0845959	−	0.996415i	$-0.526960\pi$
$491$	−3.74904	−0.169192	−0.0845959	+	0.996415i	$0.526960\pi$
$492$	9.87012	0.444979
$493$	8.59873	0.387267
$494$	−0.180590	−0.00812511
$495$	0.821286	0.0369141
$496$	43.1344	1.93679
$497$	−2.72623	−0.122288
$498$	−7.81306	−0.350112
$499$	−17.1917	−0.769605	−0.384803	−	0.922999i	$-0.625730\pi$
$499$	−17.1917	−0.769605	−0.384803	+	0.922999i	$0.625730\pi$
$500$	1.34731	0.0602534
$501$	−19.8788	−0.888121
$502$	−15.4842	−0.691095
$503$	−40.0900	−1.78752	−0.893762	−	0.448541i	$-0.851944\pi$
$503$	−40.0900	−1.78752	−0.893762	+	0.448541i	$0.851944\pi$
$504$	1.73621	0.0773369
$505$	14.3789	0.639855
$506$	−5.98992	−0.266284
$507$	16.1638	0.717859
$508$	−10.8534	−0.481544
$509$	−31.3980	−1.39169	−0.695846	−	0.718191i	$-0.744970\pi$
$509$	−31.3980	−1.39169	−0.695846	+	0.718191i	$0.744970\pi$
$510$	3.64128	0.161239
$511$	2.51473	0.111245
$512$	−20.2522	−0.895029
$513$	−27.1783	−1.19995
$514$	37.6557	1.66092
$515$	6.39271	0.281697
$516$	−10.4582	−0.460397
$517$	5.55534	0.244323
$518$	1.30975	0.0575472
$519$	16.4097	0.720305
$520$	−0.0240180	−0.00105326
$521$	21.3051	0.933393	0.466697	−	0.884417i	$-0.345444\pi$
$521$	21.3051	0.933393	0.466697	+	0.884417i	$0.345444\pi$
$522$	14.2901	0.625460
$523$	−18.4962	−0.808783	−0.404392	−	0.914586i	$-0.632517\pi$
$523$	−18.4962	−0.808783	−0.404392	+	0.914586i	$0.632517\pi$
$524$	7.94018	0.346868
$525$	1.24341	0.0542668
$526$	15.3813	0.670657
$527$	−14.1499	−0.616378
$528$	−3.42710	−0.149145
$529$	10.5930	0.460566
$530$	19.9839	0.868045
$531$	1.81253	0.0786572
$532$	6.61198	0.286666
$533$	0.118501	0.00513285
$534$	34.1742	1.47886
$535$	6.07116	0.262479
$536$	−14.6241	−0.631667
$537$	24.5254	1.05835
$538$	17.3780	0.749218
$539$	−0.564870	−0.0243307
$540$	7.46147	0.321091
$541$	31.4952	1.35409	0.677043	−	0.735943i	$-0.263261\pi$
$541$	31.4952	1.35409	0.677043	+	0.735943i	$0.263261\pi$
$542$	−32.0356	−1.37605
$543$	−31.3532	−1.34549
$544$	10.4663	0.448740
$545$	1.99421	0.0854226
$546$	0.0457553	0.00195815
$547$	36.7250	1.57025	0.785124	−	0.619338i	$-0.212599\pi$
$547$	36.7250	1.57025	0.785124	+	0.619338i	$0.212599\pi$
$548$	8.22889	0.351521
$549$	−7.80016	−0.332903
$550$	1.03347	0.0440672
$551$	−26.3637	−1.12313
$552$	8.60586	0.366290
$553$	7.50967	0.319344
$554$	23.8677	1.01404
$555$	−0.890133	−0.0377840
$556$	−16.5941	−0.703748
$557$	10.0766	0.426960	0.213480	−	0.976947i	$-0.431520\pi$
$557$	10.0766	0.426960	0.213480	+	0.976947i	$0.431520\pi$
$558$	−23.5154	−0.995488
$559$	−0.125562	−0.00531069
$560$	4.87938	0.206191
$561$	1.12423	0.0474650
$562$	−35.2622	−1.48745
$563$	42.6065	1.79565	0.897824	−	0.440354i	$-0.145147\pi$
$563$	42.6065	1.79565	0.897824	+	0.440354i	$0.145147\pi$
$564$	16.4756	0.693749
$565$	13.1823	0.554584
$566$	−37.6255	−1.58152
$567$	2.52425	0.106009
$568$	3.25550	0.136598
$569$	−2.21916	−0.0930318	−0.0465159	−	0.998918i	$-0.514812\pi$
$569$	−2.21916	−0.0930318	−0.0465159	+	0.998918i	$0.514812\pi$
$570$	−11.1642	−0.467615
$571$	37.2161	1.55744	0.778722	−	0.627370i	$-0.215868\pi$
$571$	37.2161	1.55744	0.778722	+	0.627370i	$0.215868\pi$
$572$	0.0153072	0.000640026 0
$573$	13.0646	0.545780
$574$	−10.7793	−0.449918
$575$	−5.79595	−0.241708
$576$	3.20521	0.133550
$577$	−5.48268	−0.228247	−0.114123	−	0.993467i	$-0.536406\pi$
$577$	−5.48268	−0.228247	−0.114123	+	0.993467i	$0.536406\pi$
$578$	26.4152	1.09873
$579$	7.69875	0.319949
$580$	7.23783	0.300534
$581$	3.43447	0.142486
$582$	−14.7320	−0.610660
$583$	6.16994	0.255533
$584$	−3.00294	−0.124263
$585$	0.0292433	0.00120906
$586$	44.5834	1.84172
$587$	42.9295	1.77189	0.885945	−	0.463790i	$-0.153511\pi$
$587$	42.9295	1.77189	0.885945	+	0.463790i	$0.153511\pi$
$588$	−1.67525	−0.0690863
$589$	43.3834	1.78758
$590$	2.28080	0.0938992
$591$	13.5746	0.558385
$592$	−3.49306	−0.143564
$593$	10.5945	0.435063	0.217531	−	0.976053i	$-0.430200\pi$
$593$	10.5945	0.435063	0.217531	+	0.976053i	$0.430200\pi$
$594$	5.72340	0.234834
$595$	−1.60064	−0.0656197
$596$	7.51465	0.307812
$597$	−16.0676	−0.657604
$598$	−0.213281	−0.00872171
$599$	−16.1705	−0.660708	−0.330354	−	0.943857i	$-0.607168\pi$
$599$	−16.1705	−0.660708	−0.330354	+	0.943857i	$0.607168\pi$
$600$	−1.48481	−0.0606169
$601$	2.75964	0.112568	0.0562839	−	0.998415i	$-0.482075\pi$
$601$	2.75964	0.112568	0.0562839	+	0.998415i	$0.482075\pi$
$602$	11.4215	0.465507
$603$	17.8057	0.725106
$604$	−7.48527	−0.304571
$605$	−10.6809	−0.434241
$606$	32.7106	1.32878
$607$	45.9094	1.86340	0.931702	−	0.363224i	$-0.118324\pi$
$607$	45.9094	1.86340	0.931702	+	0.363224i	$0.118324\pi$
$608$	−32.0897	−1.30141
$609$	6.67967	0.270674
$610$	−9.81535	−0.397412
$611$	0.197807	0.00800242
$612$	−3.13549	−0.126745
$613$	17.9374	0.724484	0.362242	−	0.932084i	$-0.382011\pi$
$613$	17.9374	0.724484	0.362242	+	0.932084i	$0.382011\pi$
$614$	14.0406	0.566633
$615$	7.32581	0.295405
$616$	0.674535	0.0271778
$617$	17.7185	0.713319	0.356659	−	0.934234i	$-0.383916\pi$
$617$	17.7185	0.713319	0.356659	+	0.934234i	$0.383916\pi$
$618$	14.5428	0.584995
$619$	2.66481	0.107108	0.0535539	−	0.998565i	$-0.482945\pi$
$619$	2.66481	0.107108	0.0535539	+	0.998565i	$0.482945\pi$
$620$	−11.9104	−0.478333
$621$	−32.0983	−1.28806
$622$	52.0230	2.08593
$623$	−15.0223	−0.601856
$624$	−0.122028	−0.00488501
$625$	1.00000	0.0400000
$626$	16.9163	0.676112
$627$	−3.44688	−0.137655
$628$	−3.69774	−0.147556
$629$	1.14587	0.0456887
$630$	−2.66007	−0.105980
$631$	−24.9203	−0.992063	−0.496032	−	0.868305i	$-0.665210\pi$
$631$	−24.9203	−0.992063	−0.496032	+	0.868305i	$0.665210\pi$
$632$	−8.96761	−0.356712
$633$	−31.9052	−1.26812
$634$	−11.3455	−0.450587
$635$	−8.05565	−0.319679
$636$	18.2984	0.725578
$637$	−0.0201131	−0.000796912 0
$638$	5.55185	0.219800
$639$	−3.96376	−0.156804
$640$	−9.04443	−0.357512
$641$	−3.64037	−0.143786	−0.0718930	−	0.997412i	$-0.522904\pi$
$641$	−3.64037	−0.143786	−0.0718930	+	0.997412i	$0.522904\pi$
$642$	13.8112	0.545086
$643$	8.23472	0.324746	0.162373	−	0.986729i	$-0.448085\pi$
$643$	8.23472	0.324746	0.162373	+	0.986729i	$0.448085\pi$
$644$	7.80893	0.307715
$645$	−7.76230	−0.305640
$646$	14.3716	0.565443
$647$	−17.3910	−0.683710	−0.341855	−	0.939753i	$-0.611055\pi$
$647$	−17.3910	−0.683710	−0.341855	+	0.939753i	$0.611055\pi$
$648$	−3.01432	−0.118413
$649$	0.704188	0.0276418
$650$	0.0367983	0.00144335
$651$	−10.9919	−0.430806
$652$	−27.5275	−1.07806
$653$	11.8635	0.464255	0.232127	−	0.972685i	$-0.425431\pi$
$653$	11.8635	0.464255	0.232127	+	0.972685i	$0.425431\pi$
$654$	4.53662	0.177396
$655$	5.89337	0.230273
$656$	28.7479	1.12242
$657$	3.65626	0.142644
$658$	−17.9933	−0.701450
$659$	13.3457	0.519874	0.259937	−	0.965626i	$-0.416298\pi$
$659$	13.3457	0.519874	0.259937	+	0.965626i	$0.416298\pi$
$660$	0.946300	0.0368347
$661$	30.3552	1.18068	0.590341	−	0.807154i	$-0.298993\pi$
$661$	30.3552	1.18068	0.590341	+	0.807154i	$0.298993\pi$
$662$	−49.3079	−1.91641
$663$	0.0400301	0.00155464
$664$	−4.10125	−0.159159
$665$	4.90755	0.190307
$666$	1.90430	0.0737901
$667$	−31.1362	−1.20560
$668$	21.5399	0.833405
$669$	29.9682	1.15864
$670$	22.4059	0.865615
$671$	−3.03045	−0.116989
$672$	8.13046	0.313639
$673$	15.6074	0.601622	0.300811	−	0.953684i	$-0.402743\pi$
$673$	15.6074	0.601622	0.300811	+	0.953684i	$0.402743\pi$
$674$	37.1764	1.43198
$675$	5.53806	0.213160
$676$	−17.5145	−0.673633
$677$	−23.8889	−0.918126	−0.459063	−	0.888404i	$-0.651815\pi$
$677$	−23.8889	−0.918126	−0.459063	+	0.888404i	$0.651815\pi$
$678$	29.9884	1.15170
$679$	6.47589	0.248522
$680$	1.91139	0.0732984
$681$	−13.6581	−0.523380
$682$	−9.13599	−0.349835
$683$	−5.33676	−0.204206	−0.102103	−	0.994774i	$-0.532557\pi$
$683$	−5.33676	−0.204206	−0.102103	+	0.994774i	$0.532557\pi$
$684$	9.61341	0.367578
$685$	6.10766	0.233362
$686$	1.82956	0.0698531
$687$	1.24341	0.0474390
$688$	−30.4608	−1.16131
$689$	0.219691	0.00836957
$690$	−13.1852	−0.501951
$691$	50.4865	1.92060	0.960299	−	0.278973i	$-0.0899941\pi$
$691$	50.4865	1.92060	0.960299	+	0.278973i	$0.0899941\pi$
$692$	−17.7809	−0.675928
$693$	−0.821286	−0.0311981
$694$	−36.2672	−1.37668
$695$	−12.3165	−0.467192
$696$	−7.97647	−0.302347
$697$	−9.43050	−0.357206
$698$	−45.9937	−1.74089
$699$	−19.3588	−0.732219
$700$	−1.34731	−0.0509235
$701$	−49.5715	−1.87229	−0.936145	−	0.351613i	$-0.885633\pi$
$701$	−49.5715	−1.87229	−0.936145	+	0.351613i	$0.885633\pi$
$702$	0.203791	0.00769161
$703$	−3.51323	−0.132504
$704$	1.24526	0.0469324
$705$	12.2286	0.460554
$706$	61.3093	2.30741
$707$	−14.3789	−0.540776
$708$	2.08843	0.0784881
$709$	−3.11558	−0.117008	−0.0585040	−	0.998287i	$-0.518633\pi$
$709$	−3.11558	−0.117008	−0.0585040	+	0.998287i	$0.518633\pi$
$710$	−4.98781	−0.187189
$711$	10.9186	0.409479
$712$	17.9388	0.672284
$713$	51.2370	1.91884
$714$	−3.64128	−0.136272
$715$	0.0113613	0.000424889 0
$716$	−26.5748	−0.993146
$717$	−10.2955	−0.384493
$718$	16.6860	0.622717
$719$	34.6751	1.29316	0.646581	−	0.762845i	$-0.276198\pi$
$719$	34.6751	1.29316	0.646581	+	0.762845i	$0.276198\pi$
$720$	7.09431	0.264389
$721$	−6.39271	−0.238077
$722$	−9.30156	−0.346168
$723$	2.61276	0.0971696
$724$	33.9731	1.26260
$725$	5.37206	0.199513
$726$	−24.2980	−0.901782
$727$	17.3888	0.644916	0.322458	−	0.946584i	$-0.395491\pi$
$727$	17.3888	0.644916	0.322458	+	0.946584i	$0.395491\pi$
$728$	0.0240180	0.000890165 0
$729$	24.3283	0.901048
$730$	4.60086	0.170285
$731$	9.99240	0.369582
$732$	−8.98749	−0.332187
$733$	25.0684	0.925923	0.462962	−	0.886378i	$-0.346787\pi$
$733$	25.0684	0.925923	0.462962	+	0.886378i	$0.346787\pi$
$734$	9.69344	0.357792
$735$	−1.24341	−0.0458638
$736$	−37.8989	−1.39697
$737$	6.91772	0.254817
$738$	−15.6724	−0.576909
$739$	36.9120	1.35783	0.678915	−	0.734217i	$-0.262450\pi$
$739$	36.9120	1.35783	0.678915	+	0.734217i	$0.262450\pi$
$740$	0.964514	0.0354562
$741$	−0.122732	−0.00450868
$742$	−19.9839	−0.733632
$743$	19.2930	0.707793	0.353896	−	0.935285i	$-0.384857\pi$
$743$	19.2930	0.707793	0.353896	+	0.935285i	$0.384857\pi$
$744$	13.1259	0.481219
$745$	5.57753	0.204345
$746$	−22.3927	−0.819855
$747$	4.99351	0.182703
$748$	−1.21817	−0.0445408
$749$	−6.07116	−0.221835
$750$	2.27489	0.0830674
$751$	−53.6125	−1.95635	−0.978174	−	0.207789i	$-0.933373\pi$
$751$	−53.6125	−1.95635	−0.978174	+	0.207789i	$0.933373\pi$
$752$	47.9873	1.74992
$753$	−10.5234	−0.383493
$754$	0.197683	0.00719919
$755$	−5.55572	−0.202193
$756$	−7.46147	−0.271371
$757$	41.7309	1.51673	0.758367	−	0.651828i	$-0.225998\pi$
$757$	41.7309	1.51673	0.758367	+	0.651828i	$0.225998\pi$
$758$	−26.9947	−0.980493
$759$	−4.07086	−0.147763
$760$	−5.86031	−0.212576
$761$	29.4408	1.06723	0.533613	−	0.845728i	$-0.320834\pi$
$761$	29.4408	1.06723	0.533613	+	0.845728i	$0.320834\pi$
$762$	−18.3258	−0.663872
$763$	−1.99421	−0.0721953
$764$	−14.1563	−0.512155
$765$	−2.32723	−0.0841411
$766$	3.27120	0.118193
$767$	0.0250738	0.000905363 0
$768$	−26.0573	−0.940262
$769$	46.1592	1.66454	0.832272	−	0.554368i	$-0.187040\pi$
$769$	46.1592	1.66454	0.832272	+	0.554368i	$0.187040\pi$
$770$	−1.03347	−0.0372436
$771$	25.5915	0.921656
$772$	−8.34207	−0.300238
$773$	−1.15571	−0.0415681	−0.0207841	−	0.999784i	$-0.506616\pi$
$773$	−1.15571	−0.0415681	−0.0207841	+	0.999784i	$0.506616\pi$
$774$	16.6062	0.596898
$775$	−8.84014	−0.317547
$776$	−7.73313	−0.277603
$777$	0.890133	0.0319333
$778$	−12.5762	−0.450880
$779$	28.9139	1.03595
$780$	0.0336946	0.00120646
$781$	−1.53996	−0.0551043
$782$	16.9733	0.606962
$783$	29.7508	1.06321
$784$	−4.87938	−0.174263
$785$	−2.74454	−0.0979569
$786$	13.4068	0.478204
$787$	20.2872	0.723161	0.361581	−	0.932341i	$-0.382237\pi$
$787$	20.2872	0.723161	0.361581	+	0.932341i	$0.382237\pi$
$788$	−14.7089	−0.523984
$789$	10.4534	0.372152
$790$	13.7394	0.488827
$791$	−13.1823	−0.468709
$792$	0.980733	0.0348488
$793$	−0.107904	−0.00383179
$794$	−34.7011	−1.23150
$795$	13.5814	0.481684
$796$	17.4102	0.617090
$797$	52.6986	1.86668	0.933341	−	0.358991i	$-0.116879\pi$
$797$	52.6986	1.86668	0.933341	+	0.358991i	$0.116879\pi$
$798$	11.1642	0.395207
$799$	−15.7418	−0.556905
$800$	6.53885	0.231183
$801$	−21.8415	−0.771732
$802$	−37.3136	−1.31759
$803$	1.42049	0.0501282
$804$	20.5161	0.723547
$805$	5.79595	0.204280
$806$	−0.325302	−0.0114583
$807$	11.8104	0.415746
$808$	17.1705	0.604056
$809$	50.4062	1.77219	0.886095	−	0.463504i	$-0.153408\pi$
$809$	50.4062	1.77219	0.886095	+	0.463504i	$0.153408\pi$
$810$	4.61828	0.162270
$811$	15.3889	0.540378	0.270189	−	0.962807i	$-0.412914\pi$
$811$	15.3889	0.540378	0.270189	+	0.962807i	$0.412914\pi$
$812$	−7.23783	−0.253998
$813$	−21.7720	−0.763579
$814$	0.739840	0.0259314
$815$	−20.4315	−0.715684
$816$	9.71115	0.339958
$817$	−30.6367	−1.07184
$818$	−66.2477	−2.31629
$819$	−0.0292433	−0.00102184
$820$	−7.93796	−0.277206
$821$	42.4984	1.48321	0.741603	−	0.670840i	$-0.234066\pi$
$821$	42.4984	1.48321	0.741603	+	0.670840i	$0.234066\pi$
$822$	13.8943	0.484618
$823$	18.6581	0.650380	0.325190	−	0.945649i	$-0.394572\pi$
$823$	18.6581	0.650380	0.325190	+	0.945649i	$0.394572\pi$
$824$	7.63381	0.265936
$825$	0.702364	0.0244532
$826$	−2.28080	−0.0793593
$827$	12.3405	0.429120	0.214560	−	0.976711i	$-0.431168\pi$
$827$	12.3405	0.429120	0.214560	+	0.976711i	$0.431168\pi$
$828$	11.3537	0.394568
$829$	44.9215	1.56019	0.780095	−	0.625662i	$-0.215171\pi$
$829$	44.9215	1.56019	0.780095	+	0.625662i	$0.215171\pi$
$830$	6.28359	0.218106
$831$	16.2210	0.562699
$832$	0.0443395	0.00153719
$833$	1.60064	0.0554588
$834$	−28.0188	−0.970210
$835$	15.9874	0.553267
$836$	3.73491	0.129175
$837$	−48.9572	−1.69221
$838$	39.1086	1.35098
$839$	−10.2507	−0.353895	−0.176947	−	0.984220i	$-0.556622\pi$
$839$	−10.2507	−0.353895	−0.176947	+	0.984220i	$0.556622\pi$
$840$	1.48481	0.0512307
$841$	−0.140921	−0.00485935
$842$	−28.4034	−0.978846
$843$	−23.9649	−0.825395
$844$	34.5712	1.18999
$845$	−12.9996	−0.447200
$846$	−26.1611	−0.899436
$847$	10.6809	0.367001
$848$	53.2963	1.83020
$849$	−25.5710	−0.877596
$850$	−2.92847	−0.100446
$851$	−4.14922	−0.142233
$852$	−4.56712	−0.156467
$853$	48.2775	1.65299	0.826495	−	0.562944i	$-0.190331\pi$
$853$	48.2775	1.65299	0.826495	+	0.562944i	$0.190331\pi$
$854$	9.81535	0.335874
$855$	7.13527	0.244021
$856$	7.24983	0.247794
$857$	−24.6697	−0.842700	−0.421350	−	0.906898i	$-0.638444\pi$
$857$	−24.6697	−0.842700	−0.421350	+	0.906898i	$0.638444\pi$
$858$	0.0258458	0.000882361 0
$859$	−41.0058	−1.39910	−0.699550	−	0.714584i	$-0.746616\pi$
$859$	−41.0058	−1.39910	−0.699550	+	0.714584i	$0.746616\pi$
$860$	8.41092	0.286810
$861$	−7.32581	−0.249663
$862$	−42.9888	−1.46421
$863$	−23.2853	−0.792641	−0.396321	−	0.918112i	$-0.629713\pi$
$863$	−23.2853	−0.792641	−0.396321	+	0.918112i	$0.629713\pi$
$864$	36.2126	1.23198
$865$	−13.1973	−0.448723
$866$	56.4669	1.91882
$867$	17.9523	0.609691
$868$	11.9104	0.404265
$869$	4.24199	0.143900
$870$	12.2209	0.414327
$871$	0.246317	0.00834613
$872$	2.38137	0.0806434
$873$	9.41554	0.318668
$874$	−52.0400	−1.76028
$875$	−1.00000	−0.0338062
$876$	4.21280	0.142337
$877$	31.6083	1.06734	0.533668	−	0.845694i	$-0.320813\pi$
$877$	31.6083	1.06734	0.533668	+	0.845694i	$0.320813\pi$
$878$	36.1637	1.22046
$879$	30.2997	1.02198
$880$	2.75621	0.0929120
$881$	13.1276	0.442279	0.221140	−	0.975242i	$-0.429022\pi$
$881$	13.1276	0.442279	0.221140	+	0.975242i	$0.429022\pi$
$882$	2.66007	0.0895693
$883$	12.2515	0.412296	0.206148	−	0.978521i	$-0.433907\pi$
$883$	12.2515	0.412296	0.206148	+	0.978521i	$0.433907\pi$
$884$	−0.0433750	−0.00145886
$885$	1.55008	0.0521053
$886$	24.3023	0.816450
$887$	−0.876227	−0.0294208	−0.0147104	−	0.999892i	$-0.504683\pi$
$887$	−0.876227	−0.0294208	−0.0147104	+	0.999892i	$0.504683\pi$
$888$	−1.06295	−0.0356701
$889$	8.05565	0.270178
$890$	−27.4843	−0.921275
$891$	1.42587	0.0477686
$892$	−32.4724	−1.08726
$893$	48.2643	1.61510
$894$	12.6883	0.424360
$895$	−19.7243	−0.659312
$896$	9.04443	0.302153
$897$	−0.144950	−0.00483974
$898$	55.3648	1.84755
$899$	−47.4898	−1.58387
$900$	−1.95890	−0.0652967
$901$	−17.4834	−0.582456
$902$	−6.08889	−0.202738
$903$	7.76230	0.258313
$904$	15.7415	0.523556
$905$	25.2155	0.838192
$906$	−12.6387	−0.419892
$907$	3.41905	0.113528	0.0567638	−	0.998388i	$-0.481922\pi$
$907$	3.41905	0.113528	0.0567638	+	0.998388i	$0.481922\pi$
$908$	14.7994	0.491135
$909$	−20.9061	−0.693411
$910$	−0.0367983	−0.00121985
$911$	−11.8798	−0.393595	−0.196797	−	0.980444i	$-0.563054\pi$
$911$	−11.8798	−0.393595	−0.196797	+	0.980444i	$0.563054\pi$
$912$	−29.7744	−0.985928
$913$	1.94003	0.0642056
$914$	−1.21620	−0.0402284
$915$	−6.67070	−0.220526
$916$	−1.34731	−0.0445163
$917$	−5.89337	−0.194616
$918$	−16.2180	−0.535275
$919$	37.0185	1.22113	0.610565	−	0.791966i	$-0.290943\pi$
$919$	37.0185	1.22113	0.610565	+	0.791966i	$0.290943\pi$
$920$	−6.92119	−0.228185
$921$	9.54226	0.314428
$922$	34.4654	1.13506
$923$	−0.0548330	−0.00180485
$924$	−0.946300	−0.0311310
$925$	0.715882	0.0235381
$926$	18.0605	0.593505
$927$	−9.29461	−0.305275
$928$	35.1271	1.15310
$929$	53.9379	1.76965	0.884823	−	0.465928i	$-0.154279\pi$
$929$	53.9379	1.76965	0.884823	+	0.465928i	$0.154279\pi$
$930$	−20.1104	−0.659446
$931$	−4.90755	−0.160838
$932$	20.9765	0.687108
$933$	35.3558	1.15750
$934$	−17.8026	−0.582518
$935$	−0.904152	−0.0295689
$936$	0.0349206	0.00114142
$937$	8.39963	0.274404	0.137202	−	0.990543i	$-0.456189\pi$
$937$	8.39963	0.274404	0.137202	+	0.990543i	$0.456189\pi$
$938$	−22.4059	−0.731578
$939$	11.4967	0.375179
$940$	−13.2504	−0.432180
$941$	−22.1143	−0.720905	−0.360453	−	0.932777i	$-0.617378\pi$
$941$	−22.1143	−0.720905	−0.360453	+	0.932777i	$0.617378\pi$
$942$	−6.24354	−0.203426
$943$	34.1481	1.11201
$944$	6.08281	0.197979
$945$	−5.53806	−0.180153
$946$	6.45169	0.209762
$947$	−26.6071	−0.864615	−0.432307	−	0.901726i	$-0.642300\pi$
$947$	−26.6071	−0.864615	−0.432307	+	0.901726i	$0.642300\pi$
$948$	12.5806	0.408599
$949$	0.0505791	0.00164187
$950$	8.97868	0.291307
$951$	−7.71062	−0.250034
$952$	−1.91139	−0.0619485
$953$	−52.6156	−1.70439	−0.852193	−	0.523227i	$-0.824728\pi$
$953$	−52.6156	−1.70439	−0.852193	+	0.523227i	$0.824728\pi$
$954$	−29.0554	−0.940702
$955$	−10.5071	−0.340001
$956$	11.1558	0.360805
$957$	3.77314	0.121968
$958$	49.0391	1.58438
$959$	−6.10766	−0.197226
$960$	2.74109	0.0884684
$961$	47.1481	1.52091
$962$	0.0263433	0.000849341 0
$963$	−8.82709	−0.284449
$964$	−2.83109	−0.0911831
$965$	−6.19166	−0.199317
$966$	13.1852	0.424226
$967$	12.7442	0.409826	0.204913	−	0.978780i	$-0.434309\pi$
$967$	12.7442	0.409826	0.204913	+	0.978780i	$0.434309\pi$
$968$	−12.7545	−0.409946
$969$	9.76722	0.313768
$970$	11.8481	0.380418
$971$	−27.5745	−0.884909	−0.442455	−	0.896791i	$-0.645892\pi$
$971$	−27.5745	−0.884909	−0.442455	+	0.896791i	$0.645892\pi$
$972$	−18.1557	−0.582343
$973$	12.3165	0.394849
$974$	−68.0846	−2.18157
$975$	0.0250088	0.000800924 0
$976$	−26.1771	−0.837910
$977$	−19.8389	−0.634703	−0.317351	−	0.948308i	$-0.602793\pi$
$977$	−19.8389	−0.634703	−0.317351	+	0.948308i	$0.602793\pi$
$978$	−46.4795	−1.48625
$979$	−8.48565	−0.271203
$980$	1.34731	0.0430382
$981$	−2.89946	−0.0925726
$982$	6.85911	0.218883
$983$	−39.7357	−1.26737	−0.633686	−	0.773590i	$-0.718459\pi$
$983$	−39.7357	−1.26737	−0.633686	+	0.773590i	$0.718459\pi$
$984$	8.74805	0.278878
$985$	−10.9173	−0.347853
$986$	−15.7319	−0.501007
$987$	−12.2286	−0.389239
$988$	0.132988	0.00423090
$989$	−36.1827	−1.15054
$990$	−1.50260	−0.0477556
$991$	50.0491	1.58986	0.794931	−	0.606699i	$-0.207507\pi$
$991$	50.0491	1.58986	0.794931	+	0.606699i	$0.207507\pi$
$992$	−57.8044	−1.83529
$993$	−33.5106	−1.06343
$994$	4.98781	0.158204
$995$	12.9222	0.409663
$996$	5.75361	0.182310
$997$	−46.6136	−1.47627	−0.738134	−	0.674655i	$-0.764293\pi$
$997$	−46.6136	−1.47627	−0.738134	+	0.674655i	$0.764293\pi$
$998$	31.4533	0.995637
$999$	3.96460	0.125434

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.m.1.14	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.m.1.14	✓	67	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.82956 q^{2} -1.24341 q^{3} +1.34731 q^{4} +1.00000 q^{5} +2.27489 q^{6} -1.00000 q^{7} +1.19414 q^{8} -1.45394 q^{9} +O(q^{10})\)	\(q-1.82956 q^{2} -1.24341 q^{3} +1.34731 q^{4} +1.00000 q^{5} +2.27489 q^{6} -1.00000 q^{7} +1.19414 q^{8} -1.45394 q^{9} -1.82956 q^{10} -0.564870 q^{11} -1.67525 q^{12} -0.0201131 q^{13} +1.82956 q^{14} -1.24341 q^{15} -4.87938 q^{16} +1.60064 q^{17} +2.66007 q^{18} -4.90755 q^{19} +1.34731 q^{20} +1.24341 q^{21} +1.03347 q^{22} -5.79595 q^{23} -1.48481 q^{24} +1.00000 q^{25} +0.0367983 q^{26} +5.53806 q^{27} -1.34731 q^{28} +5.37206 q^{29} +2.27489 q^{30} -8.84014 q^{31} +6.53885 q^{32} +0.702364 q^{33} -2.92847 q^{34} -1.00000 q^{35} -1.95890 q^{36} +0.715882 q^{37} +8.97868 q^{38} +0.0250088 q^{39} +1.19414 q^{40} -5.89172 q^{41} -2.27489 q^{42} +6.24276 q^{43} -0.761054 q^{44} -1.45394 q^{45} +10.6041 q^{46} -9.83472 q^{47} +6.06705 q^{48} +1.00000 q^{49} -1.82956 q^{50} -1.99024 q^{51} -0.0270986 q^{52} -10.9228 q^{53} -10.1322 q^{54} -0.564870 q^{55} -1.19414 q^{56} +6.10208 q^{57} -9.82854 q^{58} -1.24664 q^{59} -1.67525 q^{60} +5.36485 q^{61} +16.1736 q^{62} +1.45394 q^{63} -2.20450 q^{64} -0.0201131 q^{65} -1.28502 q^{66} -12.2466 q^{67} +2.15655 q^{68} +7.20673 q^{69} +1.82956 q^{70} +2.72623 q^{71} -1.73621 q^{72} -2.51473 q^{73} -1.30975 q^{74} -1.24341 q^{75} -6.61198 q^{76} +0.564870 q^{77} -0.0457553 q^{78} -7.50967 q^{79} -4.87938 q^{80} -2.52425 q^{81} +10.7793 q^{82} -3.43447 q^{83} +1.67525 q^{84} +1.60064 q^{85} -11.4215 q^{86} -6.67967 q^{87} -0.674535 q^{88} +15.0223 q^{89} +2.66007 q^{90} +0.0201131 q^{91} -7.80893 q^{92} +10.9919 q^{93} +17.9933 q^{94} -4.90755 q^{95} -8.13046 q^{96} -6.47589 q^{97} -1.82956 q^{98} +0.821286 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

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